First, do the obvious things like make sure the jibs are not too loose, the toolpost is tight, etc. If that does not fix things then, the compound is probably extended too far. You want most of the cutting action to take place above, and well within, the boundaries of the carriage. If the cutting action is happening too close to the left edge of the support rails of the carriage, the downward force of cutting is trying to lift the support rails on the right side off the ways.
EDIT: BTW, that looks like a CCMT 2151 and judging by that, the piece you're cutting looks about 0.5" diameter. For soft steel, that should be spinning around 1200 RPM. This is a partial cause of the vibration because you're increasing your cutting forces by not having enough speed to perform the cut.
Ray